Why can't MLPs perform non-linear regression and classification?
In Single Perceptron / Multi-layer Perceptron(MLP), we only have linear separability because they are composed of input and output layers(some hidden layers in MLP)


This is wrong. 

A multi-layer perceptron (i.e. a feed-forward neural network) with non-linear activation functions can perform non-linear classification and regression. In fact, an MLP with one hidden layer with an arbitrary number of hidden nodes, each of them with a sigmoid (which is a non-linear function), can approximate any continuous function (up to an approximation error).

On the other hand, perceptrons can't do that. They perform only linear classification/regression.


  I thought the MLP was a non-linear classifier.


You're right, unless the MLP only uses linear activation functions. In that case, it won't be able to perform non-linear classification/regression.

(P.S.: I suggest you always question the truth and correctness of what you read on the web, especially, on sites like Medium, as you actually did!)